gdennis at mit dot edu
Voter: I don't like these spoiled elections. I heard about another voting system called Instant Runoff Voting, or IRV, that doesn't allow third-party candidates to spoil elections.
Approval Voting Advocate: Don't support IRV. There's a simpler system called Approval Voting that's much better.
V: Better than IRV? How does it work?
AVA: The ballot looks the same a normal ballot, except you're allowed to vote for as many candidates as you want. All the votes are counted and treated equally, and the candidate with the most votes wins. You just vote for each candidate you approve of. No ranking necessary.
V: Wow, that is easy. But . . . hmmm . . . wait. What exactly does it mean to "approve" of a candidate? "Approval" is kind of a vague term, isn't it?
AVA: No, not really. Just think about it. Who would you approve of in the last presidential election, for instance?
V: Well, I don't really understand what it means to "approve" of a candidate, but I'm thinking . . . let's see . . . in the last presidential election, I was a strong Nader supporter, I didn't like Kerry very much, and I really didn't like Bush. So I guess I would just approve and vote for Nader then.
AVA: No, you're supposed to approve of both Nader and Kerry.
V: But I don't think I would approve of Kerry as president. I thought you told me to only vote for the candidates I approve of.
AVA: Yes, um, well, forget what I said. You're not supposed to vote for the candidates you actually "approve" of, you're supposed to vote according to a particular strategy.
V: So Approval Voting doesn't mean vote for whom you approve? Weird. So what strategy do you have to follow?
AVA: Oh, it's very simple. If there are n candidates in the election, you should vote for a candidate i if the following formula is true
where Ui is your utility for candidate i, Uj is your utility for candidate j, and Pij is the probability you break a tie by voting for i instead of j.
V: What? How in the world do I calculate that? How do I even know what those probabilities are?
AVA: The probabilities? Oh, simple, just study some public opinion polls on the race.
V: Study some polls? How many polls and which ones? Polls can have inaccuracies, and different polls can show different results with different margins of error. Plus, in the state representative and mayoral elections I vote in, there are usually no public polls to speak of.
AVA: You'll just have to use your best approximation of what the polls would say if you had accurate ones.
V: OK, so suppose there are available and accurate polls, and I do my homework to calculate all these probabilities and compute which candidates I should vote for according to that formula. IRV already prevents the spoiler effect, so what do I get out using Approval Voting and following this strategy?
AVA: Ah, glad you asked. Yes, IRV eliminates the spoiler effect, but it doesn't prevent another problem known as the "center squeeze," where a centrist candidate can fail to win. If you use the strategy I taught you, Approval Voting prevents both the spoiler and center-squeeze effects!
V: Fair enough. But I've never heard of this center squeeze happening, and I know of dozens of elections in which the spoiler effect has elected the wrong candidate. How often does this "center squeeze" thing occur?
AVA: Well, we're not sure of its exact frequency . . .
V: Well, I'm not looking for an exact frequency. Can you tell me a recent election in which its happened?
AVA: hmm, a recent election . . . let me think . . .
V: Or what about just any election in history? Just one example to help me understand.
AVA: OK, you got me. See, we can't exactly document an example of it occurring yet.
V: So you're telling me I need to have access to accurate polls, to compute this formula for every candidate in the election, all to ward off a problem you're not even sure occurs in practice?
AVA: Well, it could still happen in theory!
V: But regardless of how often it will happen, that strategy you gave me is just too complicated for the average voter.
AVA: I do agree with you there. That's why we've come up with a simpler strategy. Of the two front-runners in any election, just vote for the one you like best and then for any candidate you like better than that front-runner.
V: Well, that still requires polls to know who two front-runners are, but yes, I agree, it is much simpler.
AVA: Thank you very much.
V: But, wait, if I follow this simpler strategy, does it still prevent the center squeeze thing?
AVA: Um, ha, funny you should ask because, uh . . . no, it doesn't. That's why you should use the more complicated one. We'll only tell the "average" folks about the simpler strategy.
V: Sounds like you're creating a stratified voting system. You and your mathematician friends will use the complex strategy, while the rest of us without as much time on our hands will be stuck with the inferior one. Remind me again why you want to use Approval instead of IRV?
AVA: Um . . . because Approval is so simple?
V: More like deceptively simple. I'm sticking with Instant Runoff Voting.